Abstract

The ‘Reflection Principle’ is what rules out predictable persuasion and biases in updating, requiring your current probabilities to match your expectation for your future ones. It’s often claimed to be a theorem when Bayesians update by conditioning on the true cell of a finite partition. It’s not. I show that it robustly fails when a Bayesian’s priors are ambiguous, i.e. are probabilistically uncertainty about what their own priors are. Contrary to recent discussions, Bayesians can be predictably persuaded and biased by information.